Download Modeling goal-directed spatial navigation in the rat based on physiological

Neural Networks 16 (2003) 577–584
www.elsevier.com/locate/neunet
2003 Special issue
Modeling goal-directed spatial navigation in the rat based on physiological
data from the hippocampal formation
Randal A. Koenea,*, Anatoli Gorchetchnikovb, Robert C. Cannonc, Michael E. Hasselmoa
a
Department of Pyschology and Program in Neuroscience, Boston University, Boston, MA 02215, USA
b
Department of Cognitive and Neural Systems, Boston University, Boston, MA 02215, USA
c
Institute of Adaptive and Neural Computation, Division of Informatics, 5 Forrest Hill, Edinburgh EH1 2QL, UK
Abstract
We investigated the importance of hippocampal theta oscillations and the significance of phase differences of theta modulation in the
cortical regions that are involved in goal-directed spatial navigation. Our models used representations of entorhinal cortex layer III (ECIII),
hippocampus and prefrontal cortex (PFC) to guide movements of a virtual rat in a virtual environment. The model encoded representations of
the environment through long-term potentiation of excitatory recurrent connections between sequentially spiking place cells in ECIII and
CA3. This encoding required buffering of place cell activity, which was achieved by a short-term memory (STM) in EC that was regulated by
theta modulation and allowed synchronized reactivation with encoding phases in ECIII and CA3. Inhibition at a specific theta phase
deactivated the oldest item in the buffer when new input was presented to a full STM buffer. A 1808 phase difference separated retrieval and
encoding in ECIII and CA3, which enabled us to simulate data on theta phase precession of place cells. Retrieval of known paths was elicited
in ECIII by input at the retrieval phase from PFC working memory for goal location, requiring strict theta phase relationships with PFC.
Known locations adjacent to the virtual rat were retrieved in CA3. Together, input from ECIII and CA3 activated predictive spiking in cells in
CA1 for the next desired place on a shortest path to a goal. Consistent with data, place cell activity in CA1 and CA3 showed smaller place
fields than in ECIII.
q 2003 Elsevier Science Ltd. All rights reserved.
Keywords: Hippocampal theta oscillation; Spatial navigation; Functional interaction
1. Introduction
The theta rhythm consists of large amplitude 3 –12 Hz
oscillations recorded in the EEG of the hippocampus of
different animal species during exploration and orientation
to stimuli (Buzsáki, Leung, & Vanderwolf, 1983). These
theta oscillations are associated with rhythmic changes in
a number of physiological variables, including neuronal
membrane potential (Fox, 1989), synaptic currents in
different layers (Brankack, Stewart, & Fox, 1993), the
magnitude of synaptic transmission (Wyble, Linster, &
Hasselmo, 1997) and the spiking activity of neurons (Fox,
Wolfson, & Ranck, 1986). In addition, extensive data
demonstrates that long-term potentiation of synaptic
strength can be induced more effectively with stimulation
at the peak of theta waves, while decreases in strength or
* Corresponding author. Tel.: þ 1-617-358-2769; fax: þ1-617-353-1424.
E-mail addresses: [email protected] (R.A. Koene), [email protected]
(A. Gorchetchnikov), [email protected] (R.C. Cannon), hasselmo@
bu.edu (M.E. Hasselmo).
no change is observed with stimulation at the trough of
the theta wave (Hasselmo, Bodelon, & Wyble, 2002;
Hölscher, Anwyl, & Rowan, 1997; Huerta & Lisman,
1993; Pavlides, Greenstein, Grudman, & Winson, 1988).
This supports the hypothesis that theta rhythm allows
separate phases of encoding and retrieval. In rats, lesions
of the fornix remove much of the amplitude of theta
rhythm. This impairs the ability to learn reversal tasks, in
which a previously rewarded behavior must be replaced
with an opposite behavior. For example, rats have
difficulty learning a right turn response after initially
learning a left turn response (M’Harzi, Palacios, Monmaur, Houcine, & Delacour, 1987). Previous analytical
work has shown how performance in behavioral tasks
such as the reversal task could depend upon specific phase
relationships between physiological variables changing
during theta rhythm oscillations (Hasselmo et al., 2002).
The simulations presented here further demonstrate the
functional role of phase relationships in entorhinal cortex
and prefrontal cortex, as well as the functional role of
other physiological properties.
0893-6080/03/$ - see front matter q 2003 Elsevier Science Ltd. All rights reserved.
doi:10.1016/S0893-6080(03)00106-0
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R.A. Koene et al. / Neural Networks 16 (2003) 577–584
We have utilized spiking network models of rat
entorhinal and hippocampal circuitry to analyze the
functional role of theta rhythm oscillations. These models
have been developed in two different software packages:
CATACOMB, developed by Cannon, Koene, and Hasselmo
(2002)) and KInNeSS, developed in the Hasselmo laboratory by Gorchetchnikov. The use of separate models
effectively tests the robustness of theoretical hypotheses
and allows analysis of individual details of function. In both
of these projects, the use of spiking neurons in network
simulations to guide movements of a virtual rat in a virtual
environment allow the network activity to be analyzed in the
same manner as spiking activity recorded from single
neurons in awake behaving rats. We will first discuss
research using CATACOMB.
Using CATACOMB, a spiking neuron model of rat
entorhinal and hippocampal circuitry (Cannon et al.,
2002) was implemented to investigate the significance of
these phasic changes while performing goal-directed
spatial navigation tasks in a T-maze. The roles of neuron
populations (ECII, ECIII, CA3, CA1) are based on
hypothesized functions of these individual regions in
spatial learning and recall tasks. Instead of static data
sets, environmental input to model networks changes in
accordance with task-specific behaviours that arise from
physical simulations driven by the network output (e.g.
when exploration of the T-maze leads to the discovery of
food-reward). A virtual rat is placed in a novel
environment, given an opportunity to learn the environment and then presented with the task to navigate to a
goal discovered in that environment.
The task was successfully learned, enabling the virtual
rat to find a shortest path to food-reward. Synchronized
learning in ECIII and CA3 was achieved with a STM buffer
that insured ordered repetition of sequences of place cell
spikes without the variability caused by differences in place
field traversal times. We improved our knowledge of the
connections between physiological and behavioural data
through our approach: studying task-specific behavioural
problems caused by the dynamic interaction of the neuronal
circuitry with the experimental environment. In this manner,
we demonstrated the well-known empirical phenomenon of
phase precession by recording simulated hippocampal place
cell firing. We also found that place fields produced in our
model exhibited the typical finer grain in CA1 and less
defined, coarser appearance in ECIII. Theta modulation in
ECIII and CA3 provided phases of encoding and retrieval
that operate in parallel without interference. Theta also
regulated episodic repetition in a STM buffer. Phase
differences betwen regions undergoing theta modulation
ensured the correctly timed propagation of activity. Theta
modulation in our model is, therefore, crucial in order to
accomplish each of these three aspects of the learning and
spatial navigation task.
2. Results
During initial encoding, a virtual rat follows predetermined exploratory trajectories in the environment (Fig.
1). Place cell activity is assigned with variable place field
sizes (Barnes McNaghton, Mizumori, Leonard, & Lei-Huey, 1990; Eichenbaum, Dudchenko, Wood, Shapiro, &
Tanila, 1999; Frank, Brown, & Wilson, 2000; McNaughton, Barnes, & O’Keefe, 1983; Muller & Kubie, 1989;
Quirk, Muller, Kubie, & Ranck, 1992). Associations
between sequential place cell activity along the trajectories as well as in the goal location is encoded on
recurrent fibres in ECIII and CA3 by LTP. During task
performance, retrieval in the spiking neuron network
produces output at the CA1 population that guides the
direction of movement.
During exploration, the interval between the initial
arrival of place cell spikes from adjacent place fields is
arbitrary. However, the window of spike intervals that elicit
effective LTP is less than 40 ms (Levy & Stewart, 1983) and
LTP elicited by the single initial spike input is not reliable
enough to produce strong Hebbian learning. Repetition of
the ordered presentation of neighbouring place cell spikes is
needed within the LTP window. A STM buffer can
accomplish this.
There are no initially known patterns and buffering
cannot be LTP-dependent, as the establishment of LTP
requires in excess of 100 ms (Bi & Poo, 1998). It is
hypothesized that intrinsic mechanisms may maintain firing
patterns, as initially proposed by Lisman (Lisman & Idiart,
1995). One such mechanism is ADP (calcium sensitive
cation currents induced by muscarinic receptor activation
(Klink & Alonso, 1997)), as shown below. Synchronized
timing can be achieved by regulating repetition through
theta modulation. This assures that STM reactivation
coincides with an encoding phase in both ECIII and CA3
(Fig. 2). Recurrent inhibition within the buffer can separate
the reactivation of sequential items to maintain order
(gamma rhythm) (Jensen & Lisman, 1996; Lisman & Idiart,
1995).
2.1. Reactivation in EC at gamma intervals within a phase
of theta oscillation may provide short-term memory
Spiking produced by afferent activity during the input
phase of the buffer is reactivated by the ADP during
subsequent repetition phases. Theta modulation of membrane potential regulates the two phases. Theta oscillations
Fig. 1. Exploratory motions of a virtual rat generate place fields and
corresponding spiking activity.
R.A. Koene et al. / Neural Networks 16 (2003) 577–584
Fig. 2. The STM buffer in ECII converts arbitrary input spikes into
synchronously repeated spike pairs for encoding in ECIII and CA3. Theta
modulation of ECII pyramidal cell membrane potentials and phase-locked
afferent and recurrent transmission modulations impose the repetition
frequency and ensure that new input enters the buffer at the theta trough.
This rhythmic modulation is regulated by a spike generator which
simulates data on theta rhythmic firing of neurons in the septum. While
the capacity is limited to two items in the current example, our STM model
can accommodate up to four items that are reactivated on the depolarizing
phase of each theta cycle. Items are separated by gamma intervals that are
imposed by a population of interneurons. Another population of
interneurons provides inhibition at the phase of the first item reactivation
when place cell spike input arrives at a full STM buffer. This ensures firstin-first-out (FIFO) replacement of STM items.
(8 Hz) are produced by regular activity originating in septal
populations (Brazhnik & Fox, 1999) believed to modulate
the GABAergic inhibition of pyramidal cells via networks
of interneurons (Alonso, Gaztelu, Bruno, & Garcia-Austt,
1987; Skaggs, McNaughton, Wilson, & Barnes, 1996;
Stewart & Fox, 1990). Recurrent gamma inhibition
produced by interneuronal networks (Bragin, Jando,
Nadasdy, & Hetke, 1995) in response to each item spike
imposes intervals that maintain the distinct and ordered
reactivation of items (Fig. 3).
Noise and slow-AHP gradually decay STM. Prior to such
decay, item replacement in the buffer is controlled by
inhibition at a specific theta phase when new input is
Fig. 3. New input is added to the STM buffer and the sequence is repeated.
Reactivation of a buffered sequence occurs when ADP and the strongly
depolarizing phase of theta modulation combine to exceed the firing
threshold. Lateral inhibition maintains the separation of items in the buffer,
as reactivation causes a recurrent interneuronal network to spike at gamma
frequency (40 Hz). These recurrent GABAergic synaptic transmissions are
enabled during the high value phase of ‘recurrent transmission’ modulation,
while synapses receiving afferent input into the buffer are enabled during
the high value phase of ‘afferent transmission’ modulation.
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received. Replacement must retire the earliest item in the
buffer (FIFO). Retirement must be rapid to avoid changes in
repetition order that could become encoded in ECIII or
CA3. This carefully timed inhibition triggered in response
to the number of items in the buffer as well as the arrival of a
new item spike (shown in Fig. 4) completes the STM model
without the problematic input timing and ADP response
characteristics required in the Jensen et al. model (Jensen,
Idiart, & Lisman, 1996).
An interneuron population receives recurrent synaptic
input from the buffer cells as well as input propagated from
sources that supply afferent input to the buffer. Synaptic
efficacies establish a gating function, such that N recurrent
item inputs elicit subthreshold potentials in the interneuronal population, but an additional N þ 1th afferent input
elicits spiking. The consequent GABAergic inhibition on
the buffer is synchronized so that its hyperpolarizing effect
delays reactivation of the earliest item in the buffer long
enough for its ADP to subside (Fig. 4). The first item drops
out of the buffer and the new item assumes the last position
in the buffered sequence.
The STM buffer bridges large intervals between the
appearance of successive place cell spikes and achieves
extended repetition of paired spiking so that strong LTP can
be established. Sequential binding is, therefore, less
dependent on the speed of place field traversal and episodic
learning proceeds with correct unidirectional heteroassociativity. The STM provides input that conforms to the
encoding requirements of ECIII and CA3.
2.2. Encoding and retrieval can take place continuously in
consecutive phases of theta
The behavioural task requires ongoing acquisition of new
associations without interference from ongoing retrieval
using the same synapses. We, therefore, hypothesize that
learning and retrieval may take place in separate phases of
theta modulation (Hasselmo et al., 2002), 1808 apart to
avoid interference between the two modes (Fig. 5). This
hypothesis is supported by phase differences in different
Fig. 4. The STM buffer replaces items in a first-in-first-out (FIFO) manner
through targeted inhibition. When activity indicates a full buffer (N spikes),
this combines with the arrival of a new item spike to trigger interneurons
synchronized to spike so that the GABAergic effect on STM neurons
suppresses firing of the first item until its ADP has decayed. The new item
reactivates near the peak of theta modulation, thereby assuming the last
position in the buffered sequence.
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Fig. 5. When afferent synaptic input from EC to CA3 and EC to CA1 is
strong encoding is favoured. When recurrent synaptic transmission in CA3
and synaptic input from CA3 to CA1 is strong retrieval is favoured.
Fig. 7. The matrix of connectivity in the model demonstrates that theta
rhythm is essential to the learning of correct paths as represented by ordered
episodes of place cell spikes. Left: Good function with theta rhythm. The
matrix on the left shows good connectivity resulting from separation of
encoding and retrieval into distinct theta phases. This allows path encoding
to take place without interference from retrieved spikes. The resulting
patterns of synapses strengthened by LTP show pairwise associations
between consecutive place cells along paths in the T-maze. Right: Poor
encoding without theta. Without theta modulation the order breaks down
and erroneous associations are formed between most locations.
synaptic input currents from EC and CA3 observed in
current source density measures (Brankack et al., 1993;
Stewart & Fox, 1990).
Phase-precession is a phenomenon recorded during in
vivo experiments of spatial learning in rats (O’Keefe &
Recce, 1993; Skaggs et al., 1996). Data from these
experiments shows that the phase of theta at which a place
cell fires gradually shifts to earlier phases as a rat traverses a
known place field, as well as during learning. In the model,
we measured the firing of cells relative to theta rhythm. As
the virtual rat enters a place field the corresponding place
cell fires at late phases of theta in CA1—predictive spiking.
As the virtual rat crosses the place field, place cell firing
becomes earlier in theta in CA1—encoding spiking (Fig. 6).
During encoding phases in the model we simulate
suppression of recurrent fiber synaptic transmission via
increased interneuron activating presynaptic GABAB channels (Hasselmo et al., 2002). This prevents interference
from retrieval of existing associations (Fig. 7). Consistent
with experimental data (Hölscher et al., 1997; Wyble,
Hyman, Goyal, & Hasselmo, 2001), induction of LTP is
rhythmically modulated to occur during the encoding phase,
but not during the retrieval phase when recurrent synaptic
transmission is strong.
Known locations adjacent to the virtual rat are retrieved
in CA3 (Fig. 8), while associative retrieval in ECIII
represents known paths (Fig. 9). A PFC STM buffer stores
the location of goals that were discovered. PFC and
hippocampus must spike synchronously.
CA1 activity (Fig. 10) depends on a combination of subthreshold contributions from both CA3 (adjacent candidates) and ECIII (association with a path to the goal).
Spiking in CA1 activates an interneuronal population that
provides recurrent inhibition to CA1. A winner-take-all
competition is accomplished (Fig. 11) in which one
successful candidate spikes to indicate the next desired
place on a shortest path to a goal.
Empirical data indicates that place fields in CA1 are
significantly smaller than place fields in EC (Barnes et al.,
1990; Frank et al., 2000; Quirk et al., 1992). Measurements
Fig. 6. Encoding and retrieval theta phases simulate theta phase precession.
Model results for each place cell in CA1 show that as the corresponding
place field is entered, the cell spikes in the retrieval phase of theta
modulation. The retrieval allows the virtual rat to predict the next desired
location on a path during navigation. As the virtual rat moves, spiking shifts
to earlier phases. Spiking of the place cell during this phase allows it to
participate in the episodic encoding of new paths.
Fig. 8. Current location drives retrieval in CA3. As the virtual rat moves up
the stem of the T-maze, a synchronization population ensures that spikes
representing current location arrive in CA3 at its retrieval phase. Strong
LTP on recurrent fibres then retrieves spikes for known adjacent locations.
Lateral inhibition through interneurons in CA3 limits the spread of
retrieval. Both the previous and next locations in the stem are retrieved.
R.A. Koene et al. / Neural Networks 16 (2003) 577–584
Fig. 9. Known goal locations in the T-maze, stored in PFC, cause spiking in
ECIII which spreads from the goal along known paths. The Goal activity
elicits spiking in ECIII at its retrieval phase in each theta cycle. Retrieval
spreads away from the goal along associated known paths via recurrent
fibres previously strengthened by LTP.
in the model show that activity is limited in CA3 and CA1,
but broad in ECIII, consistent with that data (Fig. 12)
(Cannon et al., 2002).
2.3. Phase differences in theta modulation between
prefrontal and medial temporal regions enhance functional
interaction
Given the need to propagate retrieval spikes from a
source population (e.g. ECII STM) at the encoding phase of
a target population (e.g. CA3), it is clear that specific theta
phase relationships must exist between the different regions.
In Fig. 13, the magnitude of modulation at theta frequency
in cellular membrane potentials and synaptic transmission
ratios shows the phase differences that allow PFC, ECII,
ECIII, CA3 and CA1 regions to interact successfully.
2.4. An alternative model implementation provides
additional support for our hypothesis of the role of theta
in navigation
Our theoretical model was also evaluated in a different
implementation with similar functional properties using the
KIn –NeSS simulation package. We selected single-compartment integrate-and-fire neurons in the CATACOMB
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implementation above. In contrast, in KInNeSS each neuron
consists of a dendrite compartment governed by the voltage
equation and the standard approximation of the cable
equation (Bower & Beeman, 1995), plus a soma compartment based on the canonical model of the type 1 neuron
(Ermentrout & Kopell, 1986; Hoppensteadt & Izhikevich,
1998). The details of the cell model are provided elsewhere
(Gorchetchnikov & Hasselmo, 2003), while we now
emphasize the differences between the two system
implementations.
Where a septal source of modulation at theta frequency is
assumed in the CATACOMB simulation, septal cell activity
in the KInNeSS simulation is derived from recurrent
interactions with the hippocampal area via fornix connections. Similar rhythmic behaviour and synchronization at
theta frequency emerges in both simulations. This synchronization affects neuronal activity within the hippocampus,
as well as phase-locked spiking activity in the hippocampus
and PFC. In the simulation above, ECIII learned episodes of
place cell activity that represent navigable paths. In the
KInNeSS implementation, this requisite knowledge for
navigation is provided as sets of restrictions on certain
locations. Restrictions range from absolute prohibition (an
unreachable location behind a wall) to various degrees of
aversion (e.g. a representation of the scent of a predator),
established during the exploration of the environment.
Unexplored locations remain unrestricted, so that the model
can simulate path integration behaviour and attempt to take
short-cuts through those locations.
The representation of space in the CATACOMB
simulation is continuous in terms of the appearance of
place fields during exploration and the motion directed by
activity in CA1. In the KInNeSS simulation, space is
mapped onto a two-dimensional grid of cells that form the
centers of place fields. This approach is based on results by
Trullier and Meyer (2000), who demonstrated equivalent
performance with both a priori uniformly assigned place
fields and place fields that were generated dynamically to
Fig. 10. Spiking in CA1 predicts desired next location on a shortest path to a goal. Retrieval in ECIII of known paths to the goal combines with retrieval in CA3
of known adjacent locations. Where the two most rapidly coincide, a spike is elicited in CA1.
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Fig. 11. Retrieved knowledge of paths in the T-maze and of adjacent locations causes predictive spiking that drives movement. The virtual rat is at the top of the
T-maze stem. Place cell spiking at the current location retrieves three adjacent locations (down, left, right) Synaptic responses to these spikes in CA3 cause a
slowly decaying depolarization in the corresponding cells in CA1. At the same time, a goal-spike received in ECIII elicits retrieval of known paths from the
goal location at the end of the left arm of the T-maze to the bottom of the stem, as well as to the end of the right arm. This activity coincides first with the
adjacency reponse in CA1 representing the adjacent location in the left arm of the T-maze. The resulting spike in CA1 predicts the next desired location and
suppresses further spiking through lateral inhibition. The virtual rat consequently moves into the left arm of the T-maze. There, a new current location spike in
CA3 continues the predictions that drive movement.
reflect the complexity of the environment. Similarly, the
two different implementations of our theoretical model
demonstrate its robust performance, regardless of the
method chosen to generate place fields and their layout.
Finally, the KInNeSS simulation enables us to examine
performance in the case of multiple goals in a single
environment (a linear track, a maze or an open field).
Recurrent inhibition in CA1 is critical to the behaviour of
the model, as it underlies the competitive choice of a desired
move towards the nearest goal. In a linear track or maze
with narrow arms, the recurrent CA1 inhibition of the
KInNeSS simulation results in optimal winner-take-all
competition (Fig. 14). The situation is more complicated
Fig. 12. The model replicates differences in place field sizes observed in
experiments. These plots show the locations in the T-maze at which
individual example place cells in each region were activated. The place
fields generated by spiking activity in ECIII are broad and overlapping. By
contrast, the place fields in CA1 are small and well defined.
in the open field, as multiple CA1 cells of neighbouring
locations in the general direction of the goal can spike
before the onset of the competitive inhibition. This will be
resolved through the inclusion of a head-direction system
that takes output from CA1 and computes an average
direction that can consistently drive the virtual rat’s
Fig. 13. The function of the model requires specific phase relationships
between theta rhythmic modulation of membrane potentials and synaptic
transmission in different locations. During encoding (enc.), patterns spike in
the STM buffer during the depolarized membrane phase in ECII, and are
transmitted to ECIII and CA3 at their encoding phases (less depolarized
membrane potential) via afferent synapses in their phase of strong
transmission. During retrieval (retr.), the phase of membrane depolarization
in PFC activates a goal-representation that is transmitted to ECIII. During
retrieval, recurrent fibre synapses are at the phase of full strength and cause
spiking in ECIII and CA3 neurons, which are in their phase of somatic
depolarization. This leads to the retrieval of known associations. ECIII
retrieves known paths associated with the goal-location. These are
combined in CA1 with associations retrieved in CA3 that indicate known
place fields adjacent to current location of the virtual rat.
R.A. Koene et al. / Neural Networks 16 (2003) 577–584
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learning less dependent on the speed of motion and the
timing of place cell spiking, while it maintained the order in
which place cell spikes appeared for sequence learning.
Finally, place fields in model CA1 were found to be smaller
and more defined than those in ECIII.
In our upcoming work, we are adding a system of
neocortical ‘minicolumns’ that will enable the learning of
conditional relationships and task rules. This system will
interact with the hippocampus for the retrieval of episodic
memory items. A model that extends beyond the hippocampus will allow explicit separation of the components of
behavior requiring the hippocampus from those components
which are spared after hippocampal lesions.
Acknowledgements
Fig. 14. Competitive decision making between two goals on a linear track
with six place fields. ECIII and CA3 panels show raster plots of cells
according to their locations on the track and their activity over time. The
two goals and current location (c.l.) are indicated. ECII and CA1 panels
show the recorded cell activity in respective areas. The spikes in ECIII and
CA3 marked with black circles almost coincide in time and produce a rapid
response in CA1—a correct choice. The spikes in the gray circles would
produce an incorrect choice. They are further separated in time, causing a
delayed response in CA1 that is suppressed by recurrent inhibition (black
arrowhead).
The CATACOMB simulations described here and
information about CATACOMB are available on our
Computational Neurophysiology website at http://askja.bu.
edu.
Supported by NIH R01 grants DA16454, MH60013 and
MH61492 to Hasselmo and by Conte Center Grant
MH60450.
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3. Conclusion
The model successfully enabled a virtual rat to learn its
environment and to navigate on a shortest path to a foodreward goal encountered during exploration. By modeling
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